As a publisher can I define the legal basis for my own (data processing) purposes? 

Yes. The guidelines of TCF 2.0 allow publishers to administer and save their own legal bases in their CMP for a variety of data processing purposes. This also applies explicitly for processing purposes which are not supported by the framework. This information can be found in the “Publisher TC Segment” of the TC string which serves to ensure seamless transfer of the publishers’ legal bases to the vendors with whom they work.

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